Hyperplane Arrangement Cohomology and Monomials in the Exterior Algebra
Eisenbud, David · Popescu, Sorin · Yuzvinsky, Sergey
Algebraic Geometry
Algebraic Topology
Combinatorics
15A75, 52C35, 55N45 (Primary); 55N99, 14Q99 (Secondary)
Original · EN
We show that if X is the complement of a complex hyperplane arrangement, then the homology of X has linear free resolution as a module over the exterior algebra on the first cohomology of X. We study invariants of X that can be deduced from this resolution. A key ingredient is a result of Aramova, Avramov, and Herzog [2000] on resolutions of monomial ideals in the exterior algebra. We give a new conceptual proof of this result.
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